Chapter 8 Construction of Triangles Ex 8.2

Rajasthan Board RBSE Class 9 Maths Solutions Chapter 8 Construction of Triangles Ex 8.2

Case II: To construct a triangle whose two sides and included angle is given.

Question 1.
Construct a triangle ABC where a = 4 cm, b = 5 cm and ∠C = 60°.
Solution.
Steps of construction:

1. Draw b = 5 cm as base.
   
2. With C as centre, draw an angle of 60° with the help of compass.
3. With centre C, take an arc of radius 4 cm and cut it.
4. Join B to A.
   Hence, ABC is the required triangle.

Question 2.
Construct a triangle LMN where ∠L =120°, LM = 4 cm and LN = 5 cm.
Solution.
Steps of construction:

1. Draw base LM = 4 cm.
   
2. With L as centre, draw an angle of 120° with the help of compass.
3. With L as centre, draw an arc of radius 5 cm which cuts the line segment at N.
4. Join MN.
   Hence, ∆LMN is the required triangle.

Question 3.
Construct a ∆ABC where AB = AC = 8 cm, ∠A = 15°. Draw a bisector of ∠B which meets the opposite side.
Solution.
Steps of construction:

1. Draw AB = 8 cm as base.
   
2. At A draw an angle of 75°.
3. Now taking A as centre, draw an arc of radius 8 cm which cuts the arm of the angle 75° at C. Join C to B.
4. Now draw angle bisector of ∠B which meets the opposite side AC at E (suppose).
   Hence, ∆ABC is the required triangle.

Question 4.
Construct an isosceles triangle whose vertex angle is 120° and each of equal sides are 5.5 cm in length.
Solution.
Steps of construction:

1. Draw one of the equal side BC at 5.5 cm.
   
2. With B as centre, draw vertex angle 120°.
3. With centre B, draw an arc of radius 5.5 cm, which cuts at the point A.
4. Join BA and CA.
   Hence, ∆ABC is the required isosceles triangle whose vertex ∠B = 120°.